Question

Strontium-90 has a half-life of 28.8 years. If you start with a 300-gram sample of strontium-90,

how much will be left after 1440 years? ​

Answer 1

Answer: 2.66 × 10⁻¹³

Explanation:

First, use the decay formula
`A=A_oe^(kt)` where

• A is the final amount (amount left)
• A₀ is the initial amount (amount you started with)
• k is the rate of decay (you need to solve for this)
• t is the time

Given:

• A = 1/2(300) = 150
• A₀ = 300
• k = unknown
• t = 28.8

`150=300e^(28.8k)\\\\0.5=e^(28.8k)\\\\ln(0.5)=ln(e^(28.8k))\\\\ln(0.5)=28.8k\\\\\\(ln(0.5))/(28.8)=k\\\\\\\large\boxed{-0.0240676=k}\\`

Next, input the k-value and the new t-value to solve for A.

• A = unknown
• A₀ = 300
• k = -0.0240676
• t = 1440

`A=300e^(1440(-.0240676))\\\\\large\boxed{A=2.66* 10^(-13)}\\`